EVOLVED PREAMBLES FOR MAX-SAT HEURISTICS

Luís O. Rigo Jr., Valmir C. Barbosa

Abstract

MAX-SAT heuristics normally operate from random initial truth assignments to the variables. We consider the use of what we call preambles, which are sequences of variables with corresponding single-variable assignment actions intended to be used to determine a more suitable initial truth assignment for a given problem instance and a given heuristic. For a number of well established MAX-SAT heuristics and benchmark instances, we demonstrate that preambles can be evolved by a genetic algorithm such that the heuristics are outperformed in a significant fraction of the cases. The heuristics we consider include the well-known novelty, walksat-tabu, and adaptnovelty+. Our benchmark instances are those of the 2004 SAT competition and those of the 2008 MAX-SAT evaluation.

References

  1. Argelich, J., Li, C. M., Manyà, F., and Planes, J. (2008). Third Max-SAT evaluation. URL http:// www.maxsat.udl.cat/08/.
  2. Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., and Protasi, M. (1999). Complexity and Approximation: Combinatorial Optimization Problems and their Approximability Properties. Springer-Verlag, Berlin, Germany.
  3. Barbosa, V. C. (1993). Massively Parallel Models of Computation. Ellis Horwood, Chichester, UK.
  4. Barbosa, V. C. and Gafni, E. (1989). A distributed implementation of simulated annealing. Journal of Parallel and Distributed Computing, 6:411-434.
  5. Dantsin, E., Gavrilovich, M., Hirsch, E., and Konev, B. (2001). MAX SAT approximation beyond the limits of polynomial-time approximation. Annals of Pure and Applied Logic, 113:81-94.
  6. Dechter, R. (2003). Constraint Processing. Morgan Kaufmann, San Francisco, CA.
  7. Fink, E. (1998). How to solve it automatically: Selection among problem-solving methods. In Proceedings of the Fourth International Conference on Artificial Intelligence Planning Systems, pages 128-136, Menlo Park, CA. AAAI Press.
  8. Garey, M. R. and Johnson, D. S. (1979). Computers and Intractability: A Guide to the Theory of NPCompleteness. W. H. Freeman, New York, NY.
  9. Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-6:721-741.
  10. Gent, I. P. and Walsh, T. (1993). Towards an understanding of hill-climbing procedures for SAT. In Proceedings of the Eleventh National Conference on Artificial Intelligence, pages 28-33, Menlo Park, CA. AAAI Press.
  11. Gent, I. P. and Walsh, T. (1995). Unsatisfied variables in local search. In Hallam, J., editor, Hybrid Problems, Hybrid Solutions, pages 73-85, Amsterdam, The Netherlands. IOS Press.
  12. Gomes, C. P. and Selman, B. (2001). Algorithm portfolios. Artificial Intelligence, 126:43-62.
  13. Hartmann, A. K. and Weigt, M. (2005). Phase Transitions in Combinatorial Optimization Problems: Basics, Algorithms and Statistical Mechanics. WileyVCH, Weinheim, Germany.
  14. Hoos, H. H. (2002). An adaptive noise mechanism for WalkSAT. In Proceedings of the Eighteenth National Conference on Artificial Intelligence, pages 655-660, Menlo Park, CA. AAAI Press.
  15. Hutter, F., Tompkins, D. A. D., and Hoos, H. H. (2002). Scaling and probabilistic smoothing: Efficient dynamic local search for SAT. In van Hentenryck, P., editor, Principles and Practice of Constraint Programming, volume 2470 of Lecture Notes in Computer Science, pages 233-248, Berlin, Germany. SpringerVerlag.
  16. Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220:671- 680.
  17. Lagoudakis, M. G., Littman, M. L., and Parr, R. E. (2001). Selecting the right algorithm. In Proceedings of the 2001 AAAI Fall Symposium Series: Using Uncertainty within Computation, pages 74-75, Menlo Park, CA. AAAI Press.
  18. Le Berre, D. and Simon, L. (2005). The SAT 2004 competition. In Hoos, H. H. and Mitchell, D. G., editors, Theory and Applications of Satisfiability Testing, volume 3542 of Lecture Notes in Computer Science, pages 321-344, Berlin, Germany. Springer-Verlag.
  19. Leyton-Brown, K., Nudelman, E., Andrew, G., McFadden, J., and Shoham, Y. (2003). Boosting as a metaphor for algorithm design. In Rossi, F., editor, Principles and Practice of Constraint Programming, volume 2833 of Lecture Notes in Computer Science, pages 899-903, Berlin, Germany. Springer-Verlag.
  20. Manquinho, V., Marques-Silva, J., and Planes, J. (2009). Algorithms for weighted Boolean optimization. In Kullmann, O., editor, Theory and Applications of Satisfiability Testing, volume 5584 of Lecture Notes in Computer Science, pages 495-508, Berlin, Germany. Springer-Verlag.
  21. Mazure, B., Sais, L., and Gregoire, E. (1997). Tabu search for SAT. In Proceedings of the Fourteenth National Conference on Artificial Intelligence, pages 281-285, Menlo Park, CA. AAAI Press.
  22. McAllester, D., Selman, B., and Kautz, H. (1997). Evidence for invariants in local search. In Proceedings of the Fourteenth National Conference on Artificial Intelligence, pages 321-326, Menlo Park, CA. AAAI Press.
  23. Minton, S. (1996). Automatically configuring constraint satisfaction programs: A case study. Constraints, 1:7- 43.
  24. Mitchell, M. (1996). An Introduction to Genetic Algorithms. The MIT Press, Cambridge, MA.
  25. Rice, J. R. (1976). The algorithm selection problem. In Rubinoff, M. and Yovits, M. C., editors, Advances in Computers, volume 15, pages 65-118. Academic Press, New York, NY.
  26. Russell, S. and Subramanian, D. (1995). Provably boundedoptimal agents. Journal of Artificial Intelligence Research, 2:575-609.
  27. Selman, B. and Kautz, H. (1993). Domain-independant extensions to GSAT: Solving large structured variables. In Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, pages 290-295, San Mateo, CA. Morgan Kaufmann.
  28. Selman, B., Levesque, H., and Mitchell, D. (1992). A new method for solving hard satisfiability problems. In Proceedings of the Tenth National Conference on Artificial Intelligence, pages 459-465, Menlo Park, CA. AAAI Press.
  29. Tompkins, D. A. D. and Hoos, H. H. (2004). Warped landscapes and random acts of SAT solving. In Proceedings of the Eighth International Symposium on Artificial Intelligence and Mathematics, Piscataway, NJ. RUTCOR.
  30. Tompkins, D. A. D. and Hoos, H. H. (2005). UBCSAT: An implementation and experimentation environment for SLS algorithms for SAT and MAX-SAT. In Hoos, H. H. and Mitchell, D. G., editors, Theory and Applications of Satisfiability Testing, volume 3542 of Lecture Notes in Computer Science, pages 306-320, Berlin, Germany. Springer-Verlag.
  31. Vassilevska, V., Williams, R., and Woo, S. L. M. (2006). Confronting hardness using a hybrid approach. In Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1-10, New York, NY. ACM Press.
  32. Xu, L., Hutter, F., Hoos, H. H., and Leyton-Brown, K. (2008). SATzilla: Portfolio-based algorithm selection for SAT. Journal of Artificial Intelligence Research, 32:565-606.
Download


Paper Citation


in Harvard Style

O. Rigo Jr. L. and C. Barbosa V. (2011). EVOLVED PREAMBLES FOR MAX-SAT HEURISTICS . In Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2011) ISBN 978-989-8425-83-6, pages 23-31. DOI: 10.5220/0003660400230031


in Bibtex Style

@conference{ecta11,
author={Luís O. Rigo Jr. and Valmir C. Barbosa},
title={EVOLVED PREAMBLES FOR MAX-SAT HEURISTICS},
booktitle={Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2011)},
year={2011},
pages={23-31},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003660400230031},
isbn={978-989-8425-83-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2011)
TI - EVOLVED PREAMBLES FOR MAX-SAT HEURISTICS
SN - 978-989-8425-83-6
AU - O. Rigo Jr. L.
AU - C. Barbosa V.
PY - 2011
SP - 23
EP - 31
DO - 10.5220/0003660400230031